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ALBANY — For the second time in four years, the state’s largest teachers union has decided not to endorse Gov. Cuomo.

New York State United Teachers disclosed Thursday that it is staying out of the governor’s race — even while backing the two other statewide Democrats running for re-election, Comptroller Tom DiNapoli and Attorney General Eric Schneid­erman.

The 600,000-member union made the same decision in 2010, when all three candidates were also on the ballot and the union took a pass on Cuomo.

Cuomo and the teachers have been at odds through­out his tenure.

The union was upset at the governor for his new teacher-evaluation system, which initially tied teacher evaluations to the state’s controversial Common Core standardized tests.

Cuomo’s championing of charter schools also didn’t go over well with the union.

The teachers contributed $2.5 million to groups that had opposed Cuomo’s intervention on behalf of charters that Mayor de Blasio’s administration had booted from city buildings.